Unable to make a secure connection to the server. This may be a problem with the server, or it may be requiring a client authentication
certificate that you don't have.
Error code: ERR_SSL_PROTOCOL_ERROR

Those web sites still appear correctly in the same computer, using other web browsers, namely Google Chrome - "Version 48.0.2564.109 (64-bit)" - or Mozilla Firefox - version "44.0.2"

@muru: Thanks for the comment :-) Based on your suggestion, I posted a Question in Launchpad, a few minutes ago - answers.launchpad.net/ubuntu/+question/286379 - and someone already asked for additional information (which I just provided there) . I'll update this "Ask Ubuntu" Question with the results / conclusions of that Launchpad Question.
– ricmarquesFeb 19 '16 at 22:54

it's possible to convert a question to a bug report. You needn't have reported a bug separately.
– muruFeb 20 '16 at 4:39

@muru: Thanks for the information :-) I didn't know that it was possible to convert a Launchpad question to a bug report. Meanwhile, my Bug report has the information that 12 other users have the same issue. So, I'll post an answer here and update it according to the progress.
– ricmarquesFeb 20 '16 at 14:38

Based on the bug template, you've indicated you're running version
"37.0.2062.120", which is no longer supported, and has a number of
critical security bugs. You should upgrade to the latest version of
Chrome, which is Chrome 48.

If you're running a version provided by another party, such as your
distro, please inform them that they're distributing an insecure
version.

This issue seems to be fixed by Software Updates to Chromium that were made available today! :-) For the Bug 1520568 "All queries fails when 'google' is used: ERR_SSL_PROTOCOL_ERROR", the user "Marc Deslauriers (mdeslaur)" and the bot "Launchpad Janitor (janitor)" added information regarding a patch made available today and reported that "This bug was fixed in the package chromium-browser - 37.0.2062.120-0ubuntu0.12.04.2". The Status of that Bug got consequently changed from "Confirmed" to "Fix Released".

And, in fact, the "Update Manager" was "filled" with several available updates, including the 3 patches below for Chromium. I tested closing "Chromium" and then selecting only those 3 patches, installed them and then started Chromium again, to see if those patches were enough to solve the problem... and they were enough! :-)

So now, Chromium is now again able to open Google web sites. Obviously, I suggest that you also install the other available patches/Security updates. For now, I installed only the 3 available patches for chromium, because I wanted to see if those were enough to solve the issue.

Under these circumstances, I believe that I can now mark this question as answered :-)

Update information for Chromium packages:

Chromium browser
chromium-browser (Size: 45,4 MB)

Changes for the versions:
Installed version: 37.0.2062.120-0ubuntu0.12.04.1~pkg917
Available version: 37.0.2062.120-0ubuntu0.12.04.2

Thank you for your interest in this question.
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